Compact periods of Eisenstein series of orthogonal groups of rank one Joao Pedro Boavida Primary 11F67Secondary 11R4211S40Eisenstein seriesperiodautomorphicL-functionorthogonal group Fix a number field $k$ with its adele ring $\mathbb{A}$. Let $G=\mathrm{O}(n+3)$ be an orthogonal group of $k$-rank $1$ and $H=\mathrm{O}(n+2)$ a $k$-anisotropic subgroup. We unwind the global period \[ (E_{\phi},F)_H=\int_{H_k\setminus H_{\mathbb{A}}}E_{\phi}\cdot\bar{F} \] of a spherical Eisenstein series $E_{\phi}$ of $G$ against a cuspform $F$ of $H$ into an Euler product and evaluate the local factors at odd primes. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.4997 10.1512/iumj.2013.62.4997 en Indiana Univ. Math. J. 62 (2013) 869 - 890 state-of-the-art mathematics http://iumj.org/access/